King's Aurora journal now looks to be the source of the lively "Mystery of Whaling" account, first published in the Nantucket Inquirer and widely circulated in 1841-1842. The Mystery of Whaling was reprinted in, for one example, The Friend: A Religious and Literary Journal - Volume 15.

He presents the spyglass, an unequivocal smile separating his lips, and his eyes rolling with joy, though trying to preserve his dignity and imitate the coolness of the captain. With the spyglass on his shoulder the captain goes aloft and looks through his tube, to determine whether it is a sperm whale or some other kind...the boatsteerers look to the boats to see that every thing is in its place. Superfluous clothing is thrown aside. Belts are buckled on and suspenders thrown off. The cooper must stop working...lest the noise should reach the whales and alarm them. The boys are strung out on the lower yards, and have just caught sight of the spout. “There she Blows—blows-—blows,” becomes more frequent and less loud. Now they are seen from the deck. A few minutes have elapsed and the captain is coming down. He passes aft to the quarter deck...The mate is standing by the captain. The latter speaks. “Let the main-yard come aback, Mr. A.” “Haul the main-yard aback,” says the mate. It is done, and the ship is stationary.—“Stand by the boats.” ... "Lower away gently.” The boats are in the water and the crews tumble in as they may.

Mistery/Mystery of Whaling:

He presents the glass, an unequivocal smile separating his lips, and his eyes rolling with joy, though trying to preserve his dignity and imitate the coolness of the captain. With the spyglass on his shoulder the captain goes aloft and looks through his tube, to determine whether it is a sperm whale or some other kind, of which there are several, and although the appearance of their spout is somewhat different, they cannot always be distinguished by even a practised eye at any great distance. If the captain is satisfied of its being a sperm whale, he calls out “get the boats ready.” “Ay, ay, sir,” answers the mate from the deck. The watch below are called up; the boatsteerers look to the boats to see that every thing is in its place; superfluous clothing is thrown aside; belts are buckled on and suspenders thrown off. The cooper must stop working (in some ships) lest the noise should reach the whales and alarm them. The boys are strung out on the lower yards, and have just caught sight of the spout. “There she blows—blows-—blows,” becomes more frequent and less loud. Now they are seen from the deck. A few minutes have elapsed, and the captain is coming down. He passes aft to the quarter deck. The whales are getting near —perhaps within a quarter of a mile. The mate is standing by the captain. The latter speaks. “Let the main-yard come aback, Mr. A.” “Haul the main-yard aback,” says the mate. It is done, and the ship is stationary.—“Stand by the boats.” The crews group about their several boats, ready to jump in. The three mates are in the sterns of their different boats, with a boatsteerer in the head of each. Six men are at the different falls, ready to lower. The captain gives the word— “now lower away gently.” One after the other the boats drop into the water and are cleared from the tackles. The crews tumble in as they may and shove off. --from The Mistery of Whaling in the Nantucket Inquirer (June 12, 1841).

As documented in Rough Medicine, the Nantucket Historical Association has the Aurora journal of John B. King which is available on microfilm.

Further exploration in the wonderful NHA Manuscripts Database yields a more detailed description. One entry finds Dr. King trying to look on the bright side but dead tired "of this ignoble and disgusting voyage" after too elusive whales:

"Time moves with leaden wings – vain are the endeavors inspired by philosophical thoughts to feel contented and cheerful on board a whale ship; but courage and look ahead – one half of this ignoble and disgusting voyage has passed with its train of troubles and grievances. We are now in cold and boisterous weather, reefed topsails and main sail fouled – see whales frequently but not very successful in getting them, 8/4/39." --Nantucket Historical Association Manuscript Record, quote from the Aurora journal kept by Dr. John B. King

Turns out, the vivid Mistery of Whaling material appears in one August 1840 entry and the complementary "essay" or expansion that follows the final journal entry. Apparently addressing the editor and readers of the Nantucket "Enquirer" or Inquirer, King's journal entry for August 22, 1840 offers "a more circumstantial account" of "the manner of taking a sperm whale." This portion of the journal designates the whale as "oleaginous monster," using a phrase that was revised out of the newspaper version.

John B. King's August 22, 1840 journal entry:

The voyager in his intervals of relief from duty whiles away many an hour in fabricating some token of remembrance for wife, friend or sweetheart, from jawbone and teeth of the oleaginous monster in whose possession they possess a far more threatening aspect than when converted into the polished swift or shining reel on which some fair one gaily winds her silken threads and greets the donor with her fairy smiles of long tried love.

The boat-steerer turns away and resumes his walk, beguiling the time in calculating how many more such fellows will be wanted before the joyful sound of "full ship" will be heard; or in thinking of some token of remembrance for wife, friend, or sweetheart, to be fabricated from the ivory teeth of the whale. And a far more threatening aspect they present in his wide opened jaw, than when converted into the shining reel or polished swift on which some fair one winds her threads, and greets the donor and perchance the conqueror too, with the fairy smiles of grateful love.

"A lengthy essay following the last entry in the journal. It embellishes the part of the preceding note about finding and killing whales and has details about watch assignments and crew duties during the night after the whale is brought alongside. There is nothing about cutting in the whale."

The August 22, 1840 journal entry and the expansion appended in John B. King's manuscript journal would appear to be draft versions of the newspaper sketch eventually published on June 12, 1841 in the Nantucket Inquirer as "The Mistery of Whaling."

Update: However....

A day later I see the "The Mystery of Whaling" sketch, "From the Nantucket Inquirer, " appeared in the Raleigh Register on Friday, May 27, 1842 over the initials of "C. C. R." Who is C. C. R.?

Not these guys:

The same article had previously appeared Friday, November 5, 1841 in the same newspaper under the same heading, "The Mystery of Whaling," but without any attribution other than bracketed credits to the Nantucket Inquirer.